Linked Questions
21 questions linked to/from Solving an ODE in power series
2
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1
answer
2k
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Finding power series solution for differential equation in Mathematica [duplicate]
I know this topic has been covered before, but I've tried all the solutions I can find from other users' questions and none of them have worked.
I need to find a power series solution to the ...
- 23
2
votes
2
answers
493
views
How to get the series coefficient of a function defined by a differential equation [duplicate]
I need a Taylor series approximation for $x(t)$, which is defined by the following differential equation.
$\frac{dx}{dt}=-k_1 x+(1-x)k_2 e^{-k_3 t}$, $x(0)=0$
...
- 283
2
votes
1
answer
332
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Solving for the coefficients of a series [duplicate]
Suppose I have a given series $A(z)=\Sigma a_nz^n$
I want to solve a differential equation for $B(z)$ in terms of coefficients of $a_n$ as a series. Possibly with ansatz $B(z)=\Sigma b_nz^n$ or other ...
- 89
1
vote
0
answers
625
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Solving differential equations with sums (power series) [duplicate]
I have sets of 10 differential equations, but for this purpose I'll demonstrate what I need on one example that can be solved by hand.
My equation is this:
$$4GJ\Omega(\theta)\Omega'(\theta)\xi^\...
- 677
-1
votes
1
answer
384
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How to find the power series solution of this ordinary differential equation using MMA [duplicate]
I already know that the solution of this differential equation $y''(x) - x*y(x) = 0$ can be expressed by the following power series:
$$y(x)=c0(1+\frac{x^{3}}{2\times3}+\frac{x^{6}}{2\times3\times5\...
9
votes
3
answers
872
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How do I find a series solution for $e^{-\frac{1}{2}f'(x)} \mathrm{cosh}( f(x) ) = ax + b$?
I am trying to approximate a function $f(x)$ satisfying a relation between $f(x)$ and its first derivative. How do I find a series solution for $$e^{-\frac{1}{2}f'(x)} \mathrm{cosh}( f(x) ) = ax + e^{-...
- 125
6
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3
answers
4k
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Solution of equation with power series (perturbation)
So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
- 61
10
votes
1
answer
982
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Trouble with shooting method for a 4th-order differential equation
I'm trying to solve the following forth-order ODE with the shooting method:
$$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3
\left[\frac{(xy^\prime)^\prime}{x} \right]^\prime \...
- 491
0
votes
2
answers
5k
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How to solve the second order differential equation [duplicate]
I've been trying to do code this for a two or so hours, and I can't seem to do it. Please help..
I am trying to solve the following second-order differential equation:
...
- 3
2
votes
2
answers
695
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DSolve not satisfying initial conditions
I am trying to solve the following nonlinear, non-homogeneous, first order ODE:
$y'(t)=\sqrt{y(t)}-B$
$y(0)=B^2$
$B=const$
In code:
...
- 121
1
vote
2
answers
1k
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Solving recursion relation from power series
I am interested in solving differential equations in the form of power series. Let's say we have following equation:
$$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon \...
- 2,396
7
votes
1
answer
691
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Trouble with shooting method for a 4th-order stiff ODE
The ODE I need to solve is
$$\left(y^3y^{\prime\prime\prime}\right)^\prime+\frac{5}{8}xy^\prime-\frac{1}{2}y+\frac{c}{y}=0$$
where $\prime$ denotes differentiation, $c$ is a constant and $0<c\le1$....
- 491
0
votes
0
answers
906
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Solving PDEs using Taylor series
I'm thinking of solving a Partial differential algebraic equation using multidimensional polynomial (i.e. Taylor series). Consider the PDAE:
$$\mathbf F \left( \mathbf x, \mathbf y, \frac{\partial ...
- 615
0
votes
2
answers
407
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Getting the coefficients of a series that solves a differential equations
I have an example from Stewart's Calculus where the equation $y'' + y = 0$ is solved using power series. The equation
...
- 3
0
votes
1
answer
239
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Differentiation of infinite series does not seem to be useful
Trying series solution of differential equations, the routine is to define a function as a series, and differentiate it.
...
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1
vote
1
answer
130
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Solving differential equation but keeping showing running
I am trying to solve this differential equation, see the command below. But the cell keeps showing that it is running without giving any answer for a very long time. Eventually I had to abort it. Does ...
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0
votes
1
answer
97
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Solving an NODE in series
How can I solve this NODE in series
y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q.
`p` and `q` are constant.
But do not know how to actually solve it with ...
- 504
3
votes
0
answers
173
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How to find a power series expansion of a function obeying a certain PDE?
Let us suppose that I have some differential operator $D_{x,y}$ acting on functions of two variables $(x,y)$. I want to solve one eigenvalue equation
$$D_{x,y}f_{ij}(x,y)=\lambda_{i,j} f_{ij}(x,y).$$
...
- 583
0
votes
1
answer
67
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Successive solutions using previously found [closed]
is there a way to use previous calculated values of solve?
solving equations based on asymptotic expansion
$x^2+x-\varepsilon=0$
$x=x_0+\varepsilon x_1 + \varepsilon^2 x_2 + \varepsilon^3 x_3$
...
- 103
0
votes
0
answers
107
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How to make a code to find Taylor series symbolic solution to four coupled nonlinear differential equations?
I am trying to modify the existing code developed by Michael E2 in this question here. His solution was for one differential equation. I like his code because it has ability to solve nonlinear ...
- 893
0
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0
answers
72
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Recurrence relation of coeeficients of power series solution to DE
Say I have a DE
$$
-\phi \left(\phi \left(\left(6975 \phi ^2-3704 \phi +160\right) \omega '(\phi )+\phi
\left(\left(6975 \phi ^2-4688 \phi +266\right) \omega ''(\phi )+\phi \left(2
\left(...
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